Computes and optionally plots profile log-likelihoods for the parameter of the
Box-Cox power family, the Yeo-Johnson power family, or for either of the parameters in a skew power family. This is a slight generalization of the
boxcox function in the MASS package that allows for families of transformations
other than the Box-Cox power family.
a formula or fitted model object of class lm or aov.
lambda
vector of values of lambda, with default (-2, 2) in steps of 0.1, where the profile
log-likelihood will be evaluated.
plotit
logical which controls whether the result should be plotted; default TRUE.
interp
logical which controls whether spline interpolation is used. Default to
TRUE if plotting with lambda of length less than 100.
eps
Tolerance for lambda = 0; defaults to 0.02.
xlab
defaults to "lambda" or "gamma".
ylab
defaults to "log-Likelihood" or for skewPower family to the appropriate label.
family
Defaults to "bcPower" for the Box-Cox power family of
transformations. If set to "yjPower" the Yeo-Johnson family, which
permits negative responses, is used. If set to skewPower the function gives the profile
log-likelihood for the parameter selected via param.
param
Relevant only to family="skewPower", produces a profile log-likelihood for the parameter selected, maximizing over the remaining parameter.
gamma
For use when the family="skewPower", param="gamma". If this is a vector of positive values, then the profile log-likelihood for the location (or start) parameter in the skew power family is evaluated at these values of gamma. If gamma is NULL, then evaulation is done at 100 equally spaced points between min(.01, gmax - 3*se) and gmax + 3*se, where gmax is the maximimul likelihood estimate of gamma, and se is its estimated standard error. See skewPower for the definition of gamma.
grid
If TRUE, the default, a light-gray background grid is put on the
graph.
...
passes arguments from methods to the default, or from the default to plot.
Details
This routine is an elaboration of the boxcox function in the
MASS package. The first 7 arguments are the same as in boxcox, and if the argument family="bcPower" is used, the result is essentially identical to the function in MASS. Two additional families are the yjPower and skewPower families that allow a few values of the response to be non-positive.
The skew power family has two parameters a power lambda and a start or location parameter gamma, and this functin can be used to obtain a profile log-likelihood for either parameter.
Value
A list of the lambda (or possibly, gamma) vector and the computed profile log-likelihood vector,
invisibly if the result is plotted. If plotit=TRUE plots log-likelihood vs
lambda and indicates a 95
lambda. If interp=TRUE, spline interpolation is used to give a smoother plot.
Author(s)
Sanford Weisberg, <sandy@umn.edu>
References
Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations.
Journal
of the Royal Statisistical Society, Series B. 26 211-46.
Cook, R. D. and Weisberg, S. (1999) Applied Regression Including
Computing
and Graphics. Wiley.
Fox, J. (2008)
Applied Regression Analysis and Generalized Linear Models,
Second Edition. Sage.
Fox, J. and Weisberg, S. (2011)
An R Companion to Applied Regression, Second Edition, Sage.
Hawkins, D. and Weisberg, S. (2015)
Combining the Box-Cox Power and Genralized Log Transformations to Accomodate Negative Responses,
submitted for publication.
Weisberg, S. (2014) Applied Linear Regression, Fourth Edition, Wiley.
Yeo, I. and Johnson, R. (2000) A new family of
power transformations to improve normality or symmetry.
Biometrika, 87, 954-959.